The gaseous state
Introduced| English | Meaning |
|---|---|
| collide/kəˈlaɪd/ | To strike or come into contact with another moving or stationary object or particle. |
| pressure/ˈpreʃə/ | Force acting normally per unit area. |
| real gas/rɪəl ɡæs/ | An actual gas, whose behaviour departs from the ideal model at high pressure and low temperature. |
| ideal gas/aɪˈdɪəl ɡæs/ | A model of a gas with point particles that exert no intermolecular forces except during perfectly elastic collisions. |
| molar mass/ˈməʊlə mæs/ | The mass of one mole of a substance. |
The freedom of gases
- Gas molecules move fast in all directions and collide 碰撞 with the walls.
- The many tiny pushes add up to the gas pressure 压强.
- We model gases as ideal to make calculations simple.
Gas pressure is caused by:
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Each collision with the wall gives a tiny push; the many pushes add up to the pressure.
Ideal vs real gases 实际气体
- An ideal gas 理想气体 assumes: the particles take up zero volume, and there are no forces between them.
- A real gas follows this closely at low pressure and high temperature.
- It behaves least ideally at high pressure and low temperature (particles crowded, forces matter).
The ideal-gas model: point particles of zero volume with no forces between them
Boiling turns liquid water into steam, a change between states of matter
The gaseous state
p = k / V
Boyle's law: at constant temperature pressure ∝ 1/volume.
An ideal gas is assumed to have:
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The ideal-gas model assumes point particles (zero volume) with no intermolecular forces.
A real gas behaves LEAST like an ideal gas at:
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At high pressure and low temperature the particles are crowded, so their size and attractions matter.
Match each gas idea to its meaning.
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Pressure comes from collisions; an ideal gas ignores particle volume and forces; pV = nRT links them.
An ideal gas is assumed to have no forces between its particles and particles of negligible volume; real gases deviate most at high pressure and low temperature.
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At high pressure and low temperature the particles are close, so their real volume and attractions matter.
The ideal gas equation
- $p$ in Pa, $V$ in $\text{m}^3$, $n$ in mol, $T$ in kelvin (K), $R = 8.31\ \text{J}/(\text{K}\cdot\text{mol})$.
- Convert first: °C → K (add 273), and $\text{cm}^3$/$\text{dm}^3$ → $\text{m}^3$.
Gas pressure comes from many fast molecules colliding with the container walls
In pV = nRT, the temperature T must be in:
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T must be in kelvin; convert °C to K by adding 273 (and volumes to m³).
Finding molar mass 摩尔质量
Since $n = m/M$:
- This finds $M_r$ from the mass (or density) of a gas.
Which equation gives the molar mass of a gas?
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From pV = (m/M)RT, rearranging gives M = mRT/(pV).
You've got it
- gas pressure = sum of molecule–wall collisions
- ideal gas: zero particle volume, no forces; real gases deviate at high P, low T
- $pV = nRT$ (T in K, convert units first; $R = 8.31\ \text{J}/(\text{K}\cdot\text{mol})$)
- molar mass: $M = \dfrac{mRT}{pV}$